Is or is not A set determined by its ancestors (elements)?The set of all sets of two elements does not exist, but the set of sets of two elements of a given set does?Why is choosing elements in equivalence classes not a choice?Is the following claim true: “every ordinal has the empty set as one of its elements”Does a set R inherit proerties of its own elements?Existence of empty set and semantics of the existential quantifierDefine $A = 1,2,A $, $A$ can not be a set (Axiom of regularity). Can $A$ be a “class” or a “collection” of elements.Couple of questions on the Axiom of ExtensionalitySet Theory: Fully ordered but not well ordered set proofRussell's paradox in ZF theory : Enderton's Elements of set theory : Ch.2Mapping to or from elements of a set, when that set is an element
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Is or is not A set determined by its ancestors (elements)?
The set of all sets of two elements does not exist, but the set of sets of two elements of a given set does?Why is choosing elements in equivalence classes not a choice?Is the following claim true: “every ordinal has the empty set as one of its elements”Does a set R inherit proerties of its own elements?Existence of empty set and semantics of the existential quantifierDefine $A = 1,2,A $, $A$ can not be a set (Axiom of regularity). Can $A$ be a “class” or a “collection” of elements.Couple of questions on the Axiom of ExtensionalitySet Theory: Fully ordered but not well ordered set proofRussell's paradox in ZF theory : Enderton's Elements of set theory : Ch.2Mapping to or from elements of a set, when that set is an element
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
this post says
Axiom 1a. A set is determined by its elements
Remark 1. It is
important to notice that this axiom is a non trivial assertion about
belonging. To understand this consider an analogous situation in which
we consider human beings in the place of sets and elements, and x ∈ A
means x is an ancestor of A. Then clearly A isnotdetermined by its
ancestors.
I consider ancestors as elements here, which I am not sure I understand it the right way, if yes, "A is not determined by its ancestors" seems to be a typo, which should be "A is determined by its ancestors", is it?
let A = 'a', 'b', 'c'
is 'a' an ancestor and an element of set A? I suppose it is.
are 'a', 'b', 'c' ancestors and elements of set A? I suppose they all are.
biologically, this makes definitely sense.
My sister and I have exactly the same ancestors but we are different
people
mathematically, I cannot understand 'a', 'b', 'c' are ancestors of set A while set A is not determined the ancestors 'a', 'b', 'c'.
elementary-set-theory
asked Jul 30 at 11:37
yaojpyaojp
1478 bronze badges
$endgroup$
add a comment |
$begingroup$
this post says
Axiom 1a. A set is determined by its elements
Remark 1. It is
important to notice that this axiom is a non trivial assertion about
belonging. To understand this consider an analogous situation in which
we consider human beings in the place of sets and elements, and x ∈ A
means x is an ancestor of A. Then clearly A isnotdetermined by its
ancestors.
I consider ancestors as elements here, which I am not sure I understand it the right way, if yes, "A is not determined by its ancestors" seems to be a typo, which should be "A is determined by its ancestors", is it?
let A = 'a', 'b', 'c'
is 'a' an ancestor and an element of set A? I suppose it is.
are 'a', 'b', 'c' ancestors and elements of set A? I suppose they all are.
biologically, this makes definitely sense.
My sister and I have exactly the same ancestors but we are different
people
mathematically, I cannot understand 'a', 'b', 'c' are ancestors of set A while set A is not determined the ancestors 'a', 'b', 'c'.
elementary-set-theory
asked Jul 30 at 11:37
yaojpyaojp
1478 bronze badges
$endgroup$
2
$begingroup$
Don't take analogies too seriously.
$endgroup$
– Asaf Karagila♦
Jul 30 at 14:49
2
$begingroup$
Do you have any brothers or sisters?
$endgroup$
– fleablood
Jul 30 at 15:09
$begingroup$
"I consider ancestors as elements here" That is the problem. THe author wants you to consider ancestors as the parents and parents of a human being. The author doesn't want you to think of "ancestors" as have anything whatsoever to do with sets. The author is NOT talking about sets at all. The author is talking about human beings.
$endgroup$
– fleablood
Jul 30 at 15:42
add a comment |
$begingroup$
this post says
Axiom 1a. A set is determined by its elements
Remark 1. It is
important to notice that this axiom is a non trivial assertion about
belonging. To understand this consider an analogous situation in which
we consider human beings in the place of sets and elements, and x ∈ A
means x is an ancestor of A. Then clearly A isnotdetermined by its
ancestors.
I consider ancestors as elements here, which I am not sure I understand it the right way, if yes, "A is not determined by its ancestors" seems to be a typo, which should be "A is determined by its ancestors", is it?
let A = 'a', 'b', 'c'
is 'a' an ancestor and an element of set A? I suppose it is.
are 'a', 'b', 'c' ancestors and elements of set A? I suppose they all are.
biologically, this makes definitely sense.
My sister and I have exactly the same ancestors but we are different
people
mathematically, I cannot understand 'a', 'b', 'c' are ancestors of set A while set A is not determined the ancestors 'a', 'b', 'c'.
elementary-set-theory
asked Jul 30 at 11:37
yaojpyaojp
1478 bronze badges
$endgroup$
this post says
Axiom 1a. A set is determined by its elements
Remark 1. It is
important to notice that this axiom is a non trivial assertion about
belonging. To understand this consider an analogous situation in which
we consider human beings in the place of sets and elements, and x ∈ A
means x is an ancestor of A. Then clearly A isnotdetermined by its
ancestors.
I consider ancestors as elements here, which I am not sure I understand it the right way, if yes, "A is not determined by its ancestors" seems to be a typo, which should be "A is determined by its ancestors", is it?
let A = 'a', 'b', 'c'
is 'a' an ancestor and an element of set A? I suppose it is.
are 'a', 'b', 'c' ancestors and elements of set A? I suppose they all are.
biologically, this makes definitely sense.
My sister and I have exactly the same ancestors but we are different
people
mathematically, I cannot understand 'a', 'b', 'c' are ancestors of set A while set A is not determined the ancestors 'a', 'b', 'c'.
elementary-set-theory
elementary-set-theory
asked Jul 30 at 11:37
yaojpyaojp
1478 bronze badges
asked Jul 30 at 11:37
yaojpyaojp
1478 bronze badges
edited Jul 30 at 14:47
yaojp
asked Jul 30 at 11:37
yaojpyaojp
1478 bronze badges
asked Jul 30 at 11:37
yaojpyaojp
1478 bronze badges
asked Jul 30 at 11:37
yaojpyaojp
1478 bronze badges
1478 bronze badges
2
$begingroup$
Don't take analogies too seriously.
$endgroup$
– Asaf Karagila♦
Jul 30 at 14:49
2
$begingroup$
Do you have any brothers or sisters?
$endgroup$
– fleablood
Jul 30 at 15:09
$begingroup$
"I consider ancestors as elements here" That is the problem. THe author wants you to consider ancestors as the parents and parents of a human being. The author doesn't want you to think of "ancestors" as have anything whatsoever to do with sets. The author is NOT talking about sets at all. The author is talking about human beings.
$endgroup$
– fleablood
Jul 30 at 15:42
add a comment |
2
$begingroup$
Don't take analogies too seriously.
$endgroup$
– Asaf Karagila♦
Jul 30 at 14:49
2
$begingroup$
Do you have any brothers or sisters?
$endgroup$
– fleablood
Jul 30 at 15:09
$begingroup$
"I consider ancestors as elements here" That is the problem. THe author wants you to consider ancestors as the parents and parents of a human being. The author doesn't want you to think of "ancestors" as have anything whatsoever to do with sets. The author is NOT talking about sets at all. The author is talking about human beings.
$endgroup$
– fleablood
Jul 30 at 15:42
2
2
$begingroup$
Don't take analogies too seriously.
$endgroup$
– Asaf Karagila♦
Jul 30 at 14:49
$begingroup$
Don't take analogies too seriously.
$endgroup$
– Asaf Karagila♦
Jul 30 at 14:49
2
2
$begingroup$
Do you have any brothers or sisters?
$endgroup$
– fleablood
Jul 30 at 15:09
$begingroup$
Do you have any brothers or sisters?
$endgroup$
– fleablood
Jul 30 at 15:09
$begingroup$
"I consider ancestors as elements here" That is the problem. THe author wants you to consider ancestors as the parents and parents of a human being. The author doesn't want you to think of "ancestors" as have anything whatsoever to do with sets. The author is NOT talking about sets at all. The author is talking about human beings.
$endgroup$
– fleablood
Jul 30 at 15:42
$begingroup$
"I consider ancestors as elements here" That is the problem. THe author wants you to consider ancestors as the parents and parents of a human being. The author doesn't want you to think of "ancestors" as have anything whatsoever to do with sets. The author is NOT talking about sets at all. The author is talking about human beings.
$endgroup$
– fleablood
Jul 30 at 15:42
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
No, you are not determined by your ancestor, since you could have siblings. If I have a brother, then we have exactly the same ancestors.
You are not determined by your children either, since plenty of people in history did not have any children.
To your edit:
Do not take analogies too seriously. Stick to the definitions instead. Foregoing this idea of ancestors and people and getting back to sets and elements instead.
Note that there is no typo. So ancestors do not determine a person, whereas elements do determine a set.
answered Jul 30 at 11:42
Asaf Karagila♦Asaf Karagila
315k34 gold badges453 silver badges787 bronze badges
$endgroup$
$begingroup$
And children typically are shared between two different persons.
$endgroup$
– Mark Kamsma
Jul 30 at 11:43
$begingroup$
Sure. Also that. But arguably it's not normal that both ancestors are the biological father, or the biological mother. Normally that's a way to discern them. I guess I was thinking about that implicitly.
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:43
$begingroup$
"Do not take analogies too seriously": To be fair the author is not considering sets to be analogous to people. The author is considering the sentences "A set is determined by its elements", "A thing is determined by the pieces belonging to it" and "A person is determined by his ancestors" to be analogous. And the author wasn't attempting to show by analogy that the sentences are tautologically true, but actually the exact opposite. By analogy the sentence is not self-evident or tautologically true and can be true in some analogies and false in another.
$endgroup$
– fleablood
Jul 30 at 15:51
$begingroup$
@fleablood: The issue is that when one puts too much emphasis on the analogy (here "person" and "ancestors" for "set" and "element"), one tries to fit those familiar terms into the formal context, and that is bound to break. Even worse when one insists to do it opposite to the suggestion of the analogy, but nevertheless, these analogies always break down. So not taking them seriously is a good advice for life.
$endgroup$
– Asaf Karagila♦
Jul 30 at 15:53
$begingroup$
Agreed. Very, very, very strongly agreed! (This is why I hate the "sets are bags of groceries and the curly brackets are the bags the groceries are in" analogy.) Which could be a subtext of the authors point. In any event though, the author is trying to point out the difference between sets and people--- not the similarities.
$endgroup$
– fleablood
Jul 30 at 15:59
add a comment |
$begingroup$
The phrase
$A$ is determined by its elements
means that if you know all the elements of $A$ you know what the set $A$ is. There can't be two different sets that contain the precisely the same elements.
The phrase
$A$ is determined by its ancestors
is false. My sister and I have exactly the same ancestors but we are different people.
answered Jul 30 at 11:42
Ethan BolkerEthan Bolker
54.3k5 gold badges61 silver badges132 bronze badges
$endgroup$
$begingroup$
Are you and your sister different people, though? I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too!
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:47
$begingroup$
@AsafKaragila I said so, and I don't lie (on stackexchange).
$endgroup$
– Ethan Bolker
Jul 30 at 11:49
$begingroup$
"I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too! " This is a diversion but I think you are confusing Roman Polanski (Chinatown) with Alfred Hitchcock (everything else). .... okay... that was very off topic.
$endgroup$
– fleablood
Jul 30 at 15:13
$begingroup$
Ooh... you were talking about "Psycho" ("Mother! Oh, God! Mother! Blood! Blood!") and not "Chinatown" ("She's my sister; she's my daughter; she's my sister; she's my daughter").... Oh never mind. Way off topic.....
$endgroup$
– fleablood
Jul 30 at 16:03
add a comment |
$begingroup$
You are missing the entire point. The point is that a Set is NOT a person, and a person's ancestors are NOT its elements.
A person is not determined by its ancestors. My sister and I have the exact same ancestors. But we are not the same person.
Now you are arguing that if we called a set a "person" (and if we called a set an "elephant") and if we called the elements of a set its "ancestors" (or "pink go-go dancers") then we would say "a person is determined by its ancestor" and "an elephant is determined by its pink go-go dancers".
But that is not what the author is trying to do at all. The author is trying to point out that the true statement "A set is determined by by its elements" is not as trivial as it sounds. It sounds trivial. The elements belong to a set; a set was made by it's elements. And if a set had different elements it would be a different set. So it sounds trivial to say "a set is defined entirely by what elements it has".
But the author is trying to show it is not trivial by showing a case where it wouldn't be true. Our ancestors belong to us (we all have them); and we are all made by our ancestors (we wouldn't exist without them); and if we had different ancestors we'd be a different person. But, as we are individual human beings, it would be false to say "a person is defined entirely by what ancestors she has".
answered Jul 30 at 15:40
fleabloodfleablood
78.4k2 gold badges29 silver badges98 bronze badges
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add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
No, you are not determined by your ancestor, since you could have siblings. If I have a brother, then we have exactly the same ancestors.
You are not determined by your children either, since plenty of people in history did not have any children.
To your edit:
Do not take analogies too seriously. Stick to the definitions instead. Foregoing this idea of ancestors and people and getting back to sets and elements instead.
Note that there is no typo. So ancestors do not determine a person, whereas elements do determine a set.
answered Jul 30 at 11:42
Asaf Karagila♦Asaf Karagila
315k34 gold badges453 silver badges787 bronze badges
$endgroup$
$begingroup$
And children typically are shared between two different persons.
$endgroup$
– Mark Kamsma
Jul 30 at 11:43
$begingroup$
Sure. Also that. But arguably it's not normal that both ancestors are the biological father, or the biological mother. Normally that's a way to discern them. I guess I was thinking about that implicitly.
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:43
$begingroup$
"Do not take analogies too seriously": To be fair the author is not considering sets to be analogous to people. The author is considering the sentences "A set is determined by its elements", "A thing is determined by the pieces belonging to it" and "A person is determined by his ancestors" to be analogous. And the author wasn't attempting to show by analogy that the sentences are tautologically true, but actually the exact opposite. By analogy the sentence is not self-evident or tautologically true and can be true in some analogies and false in another.
$endgroup$
– fleablood
Jul 30 at 15:51
$begingroup$
@fleablood: The issue is that when one puts too much emphasis on the analogy (here "person" and "ancestors" for "set" and "element"), one tries to fit those familiar terms into the formal context, and that is bound to break. Even worse when one insists to do it opposite to the suggestion of the analogy, but nevertheless, these analogies always break down. So not taking them seriously is a good advice for life.
$endgroup$
– Asaf Karagila♦
Jul 30 at 15:53
$begingroup$
Agreed. Very, very, very strongly agreed! (This is why I hate the "sets are bags of groceries and the curly brackets are the bags the groceries are in" analogy.) Which could be a subtext of the authors point. In any event though, the author is trying to point out the difference between sets and people--- not the similarities.
$endgroup$
– fleablood
Jul 30 at 15:59
add a comment |
$begingroup$
No, you are not determined by your ancestor, since you could have siblings. If I have a brother, then we have exactly the same ancestors.
You are not determined by your children either, since plenty of people in history did not have any children.
To your edit:
Do not take analogies too seriously. Stick to the definitions instead. Foregoing this idea of ancestors and people and getting back to sets and elements instead.
Note that there is no typo. So ancestors do not determine a person, whereas elements do determine a set.
answered Jul 30 at 11:42
Asaf Karagila♦Asaf Karagila
315k34 gold badges453 silver badges787 bronze badges
$endgroup$
$begingroup$
And children typically are shared between two different persons.
$endgroup$
– Mark Kamsma
Jul 30 at 11:43
$begingroup$
Sure. Also that. But arguably it's not normal that both ancestors are the biological father, or the biological mother. Normally that's a way to discern them. I guess I was thinking about that implicitly.
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:43
$begingroup$
"Do not take analogies too seriously": To be fair the author is not considering sets to be analogous to people. The author is considering the sentences "A set is determined by its elements", "A thing is determined by the pieces belonging to it" and "A person is determined by his ancestors" to be analogous. And the author wasn't attempting to show by analogy that the sentences are tautologically true, but actually the exact opposite. By analogy the sentence is not self-evident or tautologically true and can be true in some analogies and false in another.
$endgroup$
– fleablood
Jul 30 at 15:51
$begingroup$
@fleablood: The issue is that when one puts too much emphasis on the analogy (here "person" and "ancestors" for "set" and "element"), one tries to fit those familiar terms into the formal context, and that is bound to break. Even worse when one insists to do it opposite to the suggestion of the analogy, but nevertheless, these analogies always break down. So not taking them seriously is a good advice for life.
$endgroup$
– Asaf Karagila♦
Jul 30 at 15:53
$begingroup$
Agreed. Very, very, very strongly agreed! (This is why I hate the "sets are bags of groceries and the curly brackets are the bags the groceries are in" analogy.) Which could be a subtext of the authors point. In any event though, the author is trying to point out the difference between sets and people--- not the similarities.
$endgroup$
– fleablood
Jul 30 at 15:59
add a comment |
$begingroup$
No, you are not determined by your ancestor, since you could have siblings. If I have a brother, then we have exactly the same ancestors.
You are not determined by your children either, since plenty of people in history did not have any children.
To your edit:
Do not take analogies too seriously. Stick to the definitions instead. Foregoing this idea of ancestors and people and getting back to sets and elements instead.
Note that there is no typo. So ancestors do not determine a person, whereas elements do determine a set.
answered Jul 30 at 11:42
Asaf Karagila♦Asaf Karagila
315k34 gold badges453 silver badges787 bronze badges
$endgroup$
No, you are not determined by your ancestor, since you could have siblings. If I have a brother, then we have exactly the same ancestors.
You are not determined by your children either, since plenty of people in history did not have any children.
To your edit:
Do not take analogies too seriously. Stick to the definitions instead. Foregoing this idea of ancestors and people and getting back to sets and elements instead.
Note that there is no typo. So ancestors do not determine a person, whereas elements do determine a set.
answered Jul 30 at 11:42
Asaf Karagila♦Asaf Karagila
315k34 gold badges453 silver badges787 bronze badges
edited Jul 30 at 15:06
answered Jul 30 at 11:42
Asaf Karagila♦Asaf Karagila
315k34 gold badges453 silver badges787 bronze badges
answered Jul 30 at 11:42
Asaf Karagila♦Asaf Karagila
315k34 gold badges453 silver badges787 bronze badges
answered Jul 30 at 11:42
Asaf Karagila♦Asaf Karagila
315k34 gold badges453 silver badges787 bronze badges
315k34 gold badges453 silver badges787 bronze badges
$begingroup$
And children typically are shared between two different persons.
$endgroup$
– Mark Kamsma
Jul 30 at 11:43
$begingroup$
Sure. Also that. But arguably it's not normal that both ancestors are the biological father, or the biological mother. Normally that's a way to discern them. I guess I was thinking about that implicitly.
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:43
$begingroup$
"Do not take analogies too seriously": To be fair the author is not considering sets to be analogous to people. The author is considering the sentences "A set is determined by its elements", "A thing is determined by the pieces belonging to it" and "A person is determined by his ancestors" to be analogous. And the author wasn't attempting to show by analogy that the sentences are tautologically true, but actually the exact opposite. By analogy the sentence is not self-evident or tautologically true and can be true in some analogies and false in another.
$endgroup$
– fleablood
Jul 30 at 15:51
$begingroup$
@fleablood: The issue is that when one puts too much emphasis on the analogy (here "person" and "ancestors" for "set" and "element"), one tries to fit those familiar terms into the formal context, and that is bound to break. Even worse when one insists to do it opposite to the suggestion of the analogy, but nevertheless, these analogies always break down. So not taking them seriously is a good advice for life.
$endgroup$
– Asaf Karagila♦
Jul 30 at 15:53
$begingroup$
Agreed. Very, very, very strongly agreed! (This is why I hate the "sets are bags of groceries and the curly brackets are the bags the groceries are in" analogy.) Which could be a subtext of the authors point. In any event though, the author is trying to point out the difference between sets and people--- not the similarities.
$endgroup$
– fleablood
Jul 30 at 15:59
add a comment |
$begingroup$
And children typically are shared between two different persons.
$endgroup$
– Mark Kamsma
Jul 30 at 11:43
$begingroup$
Sure. Also that. But arguably it's not normal that both ancestors are the biological father, or the biological mother. Normally that's a way to discern them. I guess I was thinking about that implicitly.
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:43
$begingroup$
"Do not take analogies too seriously": To be fair the author is not considering sets to be analogous to people. The author is considering the sentences "A set is determined by its elements", "A thing is determined by the pieces belonging to it" and "A person is determined by his ancestors" to be analogous. And the author wasn't attempting to show by analogy that the sentences are tautologically true, but actually the exact opposite. By analogy the sentence is not self-evident or tautologically true and can be true in some analogies and false in another.
$endgroup$
– fleablood
Jul 30 at 15:51
$begingroup$
@fleablood: The issue is that when one puts too much emphasis on the analogy (here "person" and "ancestors" for "set" and "element"), one tries to fit those familiar terms into the formal context, and that is bound to break. Even worse when one insists to do it opposite to the suggestion of the analogy, but nevertheless, these analogies always break down. So not taking them seriously is a good advice for life.
$endgroup$
– Asaf Karagila♦
Jul 30 at 15:53
$begingroup$
Agreed. Very, very, very strongly agreed! (This is why I hate the "sets are bags of groceries and the curly brackets are the bags the groceries are in" analogy.) Which could be a subtext of the authors point. In any event though, the author is trying to point out the difference between sets and people--- not the similarities.
$endgroup$
– fleablood
Jul 30 at 15:59
$begingroup$
And children typically are shared between two different persons.
$endgroup$
– Mark Kamsma
Jul 30 at 11:43
$begingroup$
And children typically are shared between two different persons.
$endgroup$
– Mark Kamsma
Jul 30 at 11:43
$begingroup$
Sure. Also that. But arguably it's not normal that both ancestors are the biological father, or the biological mother. Normally that's a way to discern them. I guess I was thinking about that implicitly.
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:43
$begingroup$
Sure. Also that. But arguably it's not normal that both ancestors are the biological father, or the biological mother. Normally that's a way to discern them. I guess I was thinking about that implicitly.
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:43
$begingroup$
"Do not take analogies too seriously": To be fair the author is not considering sets to be analogous to people. The author is considering the sentences "A set is determined by its elements", "A thing is determined by the pieces belonging to it" and "A person is determined by his ancestors" to be analogous. And the author wasn't attempting to show by analogy that the sentences are tautologically true, but actually the exact opposite. By analogy the sentence is not self-evident or tautologically true and can be true in some analogies and false in another.
$endgroup$
– fleablood
Jul 30 at 15:51
$begingroup$
"Do not take analogies too seriously": To be fair the author is not considering sets to be analogous to people. The author is considering the sentences "A set is determined by its elements", "A thing is determined by the pieces belonging to it" and "A person is determined by his ancestors" to be analogous. And the author wasn't attempting to show by analogy that the sentences are tautologically true, but actually the exact opposite. By analogy the sentence is not self-evident or tautologically true and can be true in some analogies and false in another.
$endgroup$
– fleablood
Jul 30 at 15:51
$begingroup$
@fleablood: The issue is that when one puts too much emphasis on the analogy (here "person" and "ancestors" for "set" and "element"), one tries to fit those familiar terms into the formal context, and that is bound to break. Even worse when one insists to do it opposite to the suggestion of the analogy, but nevertheless, these analogies always break down. So not taking them seriously is a good advice for life.
$endgroup$
– Asaf Karagila♦
Jul 30 at 15:53
$begingroup$
@fleablood: The issue is that when one puts too much emphasis on the analogy (here "person" and "ancestors" for "set" and "element"), one tries to fit those familiar terms into the formal context, and that is bound to break. Even worse when one insists to do it opposite to the suggestion of the analogy, but nevertheless, these analogies always break down. So not taking them seriously is a good advice for life.
$endgroup$
– Asaf Karagila♦
Jul 30 at 15:53
$begingroup$
Agreed. Very, very, very strongly agreed! (This is why I hate the "sets are bags of groceries and the curly brackets are the bags the groceries are in" analogy.) Which could be a subtext of the authors point. In any event though, the author is trying to point out the difference between sets and people--- not the similarities.
$endgroup$
– fleablood
Jul 30 at 15:59
$begingroup$
Agreed. Very, very, very strongly agreed! (This is why I hate the "sets are bags of groceries and the curly brackets are the bags the groceries are in" analogy.) Which could be a subtext of the authors point. In any event though, the author is trying to point out the difference between sets and people--- not the similarities.
$endgroup$
– fleablood
Jul 30 at 15:59
add a comment |
$begingroup$
The phrase
$A$ is determined by its elements
means that if you know all the elements of $A$ you know what the set $A$ is. There can't be two different sets that contain the precisely the same elements.
The phrase
$A$ is determined by its ancestors
is false. My sister and I have exactly the same ancestors but we are different people.
answered Jul 30 at 11:42
Ethan BolkerEthan Bolker
54.3k5 gold badges61 silver badges132 bronze badges
$endgroup$
$begingroup$
Are you and your sister different people, though? I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too!
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:47
$begingroup$
@AsafKaragila I said so, and I don't lie (on stackexchange).
$endgroup$
– Ethan Bolker
Jul 30 at 11:49
$begingroup$
"I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too! " This is a diversion but I think you are confusing Roman Polanski (Chinatown) with Alfred Hitchcock (everything else). .... okay... that was very off topic.
$endgroup$
– fleablood
Jul 30 at 15:13
$begingroup$
Ooh... you were talking about "Psycho" ("Mother! Oh, God! Mother! Blood! Blood!") and not "Chinatown" ("She's my sister; she's my daughter; she's my sister; she's my daughter").... Oh never mind. Way off topic.....
$endgroup$
– fleablood
Jul 30 at 16:03
add a comment |
$begingroup$
The phrase
$A$ is determined by its elements
means that if you know all the elements of $A$ you know what the set $A$ is. There can't be two different sets that contain the precisely the same elements.
The phrase
$A$ is determined by its ancestors
is false. My sister and I have exactly the same ancestors but we are different people.
answered Jul 30 at 11:42
Ethan BolkerEthan Bolker
54.3k5 gold badges61 silver badges132 bronze badges
$endgroup$
$begingroup$
Are you and your sister different people, though? I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too!
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:47
$begingroup$
@AsafKaragila I said so, and I don't lie (on stackexchange).
$endgroup$
– Ethan Bolker
Jul 30 at 11:49
$begingroup$
"I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too! " This is a diversion but I think you are confusing Roman Polanski (Chinatown) with Alfred Hitchcock (everything else). .... okay... that was very off topic.
$endgroup$
– fleablood
Jul 30 at 15:13
$begingroup$
Ooh... you were talking about "Psycho" ("Mother! Oh, God! Mother! Blood! Blood!") and not "Chinatown" ("She's my sister; she's my daughter; she's my sister; she's my daughter").... Oh never mind. Way off topic.....
$endgroup$
– fleablood
Jul 30 at 16:03
add a comment |
$begingroup$
The phrase
$A$ is determined by its elements
means that if you know all the elements of $A$ you know what the set $A$ is. There can't be two different sets that contain the precisely the same elements.
The phrase
$A$ is determined by its ancestors
is false. My sister and I have exactly the same ancestors but we are different people.
answered Jul 30 at 11:42
Ethan BolkerEthan Bolker
54.3k5 gold badges61 silver badges132 bronze badges
$endgroup$
The phrase
$A$ is determined by its elements
means that if you know all the elements of $A$ you know what the set $A$ is. There can't be two different sets that contain the precisely the same elements.
The phrase
$A$ is determined by its ancestors
is false. My sister and I have exactly the same ancestors but we are different people.
answered Jul 30 at 11:42
Ethan BolkerEthan Bolker
54.3k5 gold badges61 silver badges132 bronze badges
answered Jul 30 at 11:42
Ethan BolkerEthan Bolker
54.3k5 gold badges61 silver badges132 bronze badges
answered Jul 30 at 11:42
Ethan BolkerEthan Bolker
54.3k5 gold badges61 silver badges132 bronze badges
answered Jul 30 at 11:42
Ethan BolkerEthan Bolker
54.3k5 gold badges61 silver badges132 bronze badges
54.3k5 gold badges61 silver badges132 bronze badges
$begingroup$
Are you and your sister different people, though? I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too!
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:47
$begingroup$
@AsafKaragila I said so, and I don't lie (on stackexchange).
$endgroup$
– Ethan Bolker
Jul 30 at 11:49
$begingroup$
"I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too! " This is a diversion but I think you are confusing Roman Polanski (Chinatown) with Alfred Hitchcock (everything else). .... okay... that was very off topic.
$endgroup$
– fleablood
Jul 30 at 15:13
$begingroup$
Ooh... you were talking about "Psycho" ("Mother! Oh, God! Mother! Blood! Blood!") and not "Chinatown" ("She's my sister; she's my daughter; she's my sister; she's my daughter").... Oh never mind. Way off topic.....
$endgroup$
– fleablood
Jul 30 at 16:03
add a comment |
$begingroup$
Are you and your sister different people, though? I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too!
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:47
$begingroup$
@AsafKaragila I said so, and I don't lie (on stackexchange).
$endgroup$
– Ethan Bolker
Jul 30 at 11:49
$begingroup$
"I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too! " This is a diversion but I think you are confusing Roman Polanski (Chinatown) with Alfred Hitchcock (everything else). .... okay... that was very off topic.
$endgroup$
– fleablood
Jul 30 at 15:13
$begingroup$
Ooh... you were talking about "Psycho" ("Mother! Oh, God! Mother! Blood! Blood!") and not "Chinatown" ("She's my sister; she's my daughter; she's my sister; she's my daughter").... Oh never mind. Way off topic.....
$endgroup$
– fleablood
Jul 30 at 16:03
$begingroup$
Are you and your sister different people, though? I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too!
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:47
$begingroup$
Are you and your sister different people, though? I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too!
$endgroup$
– Asaf Karagila♦
Jul 30 at 11:47
$begingroup$
@AsafKaragila I said so, and I don't lie (on stackexchange).
$endgroup$
– Ethan Bolker
Jul 30 at 11:49
$begingroup$
@AsafKaragila I said so, and I don't lie (on stackexchange).
$endgroup$
– Ethan Bolker
Jul 30 at 11:49
$begingroup$
"I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too! " This is a diversion but I think you are confusing Roman Polanski (Chinatown) with Alfred Hitchcock (everything else). .... okay... that was very off topic.
$endgroup$
– fleablood
Jul 30 at 15:13
$begingroup$
"I've seen enough Hitchcock to question whether or not a person is also his mother, so surely a person can be his sister too! " This is a diversion but I think you are confusing Roman Polanski (Chinatown) with Alfred Hitchcock (everything else). .... okay... that was very off topic.
$endgroup$
– fleablood
Jul 30 at 15:13
$begingroup$
Ooh... you were talking about "Psycho" ("Mother! Oh, God! Mother! Blood! Blood!") and not "Chinatown" ("She's my sister; she's my daughter; she's my sister; she's my daughter").... Oh never mind. Way off topic.....
$endgroup$
– fleablood
Jul 30 at 16:03
$begingroup$
Ooh... you were talking about "Psycho" ("Mother! Oh, God! Mother! Blood! Blood!") and not "Chinatown" ("She's my sister; she's my daughter; she's my sister; she's my daughter").... Oh never mind. Way off topic.....
$endgroup$
– fleablood
Jul 30 at 16:03
add a comment |
$begingroup$
You are missing the entire point. The point is that a Set is NOT a person, and a person's ancestors are NOT its elements.
A person is not determined by its ancestors. My sister and I have the exact same ancestors. But we are not the same person.
Now you are arguing that if we called a set a "person" (and if we called a set an "elephant") and if we called the elements of a set its "ancestors" (or "pink go-go dancers") then we would say "a person is determined by its ancestor" and "an elephant is determined by its pink go-go dancers".
But that is not what the author is trying to do at all. The author is trying to point out that the true statement "A set is determined by by its elements" is not as trivial as it sounds. It sounds trivial. The elements belong to a set; a set was made by it's elements. And if a set had different elements it would be a different set. So it sounds trivial to say "a set is defined entirely by what elements it has".
But the author is trying to show it is not trivial by showing a case where it wouldn't be true. Our ancestors belong to us (we all have them); and we are all made by our ancestors (we wouldn't exist without them); and if we had different ancestors we'd be a different person. But, as we are individual human beings, it would be false to say "a person is defined entirely by what ancestors she has".
answered Jul 30 at 15:40
fleabloodfleablood
78.4k2 gold badges29 silver badges98 bronze badges
$endgroup$
add a comment |
$begingroup$
You are missing the entire point. The point is that a Set is NOT a person, and a person's ancestors are NOT its elements.
A person is not determined by its ancestors. My sister and I have the exact same ancestors. But we are not the same person.
Now you are arguing that if we called a set a "person" (and if we called a set an "elephant") and if we called the elements of a set its "ancestors" (or "pink go-go dancers") then we would say "a person is determined by its ancestor" and "an elephant is determined by its pink go-go dancers".
But that is not what the author is trying to do at all. The author is trying to point out that the true statement "A set is determined by by its elements" is not as trivial as it sounds. It sounds trivial. The elements belong to a set; a set was made by it's elements. And if a set had different elements it would be a different set. So it sounds trivial to say "a set is defined entirely by what elements it has".
But the author is trying to show it is not trivial by showing a case where it wouldn't be true. Our ancestors belong to us (we all have them); and we are all made by our ancestors (we wouldn't exist without them); and if we had different ancestors we'd be a different person. But, as we are individual human beings, it would be false to say "a person is defined entirely by what ancestors she has".
answered Jul 30 at 15:40
fleabloodfleablood
78.4k2 gold badges29 silver badges98 bronze badges
$endgroup$
add a comment |
$begingroup$
You are missing the entire point. The point is that a Set is NOT a person, and a person's ancestors are NOT its elements.
A person is not determined by its ancestors. My sister and I have the exact same ancestors. But we are not the same person.
Now you are arguing that if we called a set a "person" (and if we called a set an "elephant") and if we called the elements of a set its "ancestors" (or "pink go-go dancers") then we would say "a person is determined by its ancestor" and "an elephant is determined by its pink go-go dancers".
But that is not what the author is trying to do at all. The author is trying to point out that the true statement "A set is determined by by its elements" is not as trivial as it sounds. It sounds trivial. The elements belong to a set; a set was made by it's elements. And if a set had different elements it would be a different set. So it sounds trivial to say "a set is defined entirely by what elements it has".
But the author is trying to show it is not trivial by showing a case where it wouldn't be true. Our ancestors belong to us (we all have them); and we are all made by our ancestors (we wouldn't exist without them); and if we had different ancestors we'd be a different person. But, as we are individual human beings, it would be false to say "a person is defined entirely by what ancestors she has".
answered Jul 30 at 15:40
fleabloodfleablood
78.4k2 gold badges29 silver badges98 bronze badges
$endgroup$
You are missing the entire point. The point is that a Set is NOT a person, and a person's ancestors are NOT its elements.
A person is not determined by its ancestors. My sister and I have the exact same ancestors. But we are not the same person.
Now you are arguing that if we called a set a "person" (and if we called a set an "elephant") and if we called the elements of a set its "ancestors" (or "pink go-go dancers") then we would say "a person is determined by its ancestor" and "an elephant is determined by its pink go-go dancers".
But that is not what the author is trying to do at all. The author is trying to point out that the true statement "A set is determined by by its elements" is not as trivial as it sounds. It sounds trivial. The elements belong to a set; a set was made by it's elements. And if a set had different elements it would be a different set. So it sounds trivial to say "a set is defined entirely by what elements it has".
But the author is trying to show it is not trivial by showing a case where it wouldn't be true. Our ancestors belong to us (we all have them); and we are all made by our ancestors (we wouldn't exist without them); and if we had different ancestors we'd be a different person. But, as we are individual human beings, it would be false to say "a person is defined entirely by what ancestors she has".
answered Jul 30 at 15:40
fleabloodfleablood
78.4k2 gold badges29 silver badges98 bronze badges
edited Jul 30 at 15:55
answered Jul 30 at 15:40
fleabloodfleablood
78.4k2 gold badges29 silver badges98 bronze badges
answered Jul 30 at 15:40
fleabloodfleablood
78.4k2 gold badges29 silver badges98 bronze badges
answered Jul 30 at 15:40
fleabloodfleablood
78.4k2 gold badges29 silver badges98 bronze badges
78.4k2 gold badges29 silver badges98 bronze badges
add a comment |
add a comment |
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2
$begingroup$
Don't take analogies too seriously.
$endgroup$
– Asaf Karagila♦
Jul 30 at 14:49
2
$begingroup$
Do you have any brothers or sisters?
$endgroup$
– fleablood
Jul 30 at 15:09
$begingroup$
"I consider ancestors as elements here" That is the problem. THe author wants you to consider ancestors as the parents and parents of a human being. The author doesn't want you to think of "ancestors" as have anything whatsoever to do with sets. The author is NOT talking about sets at all. The author is talking about human beings.
$endgroup$
– fleablood
Jul 30 at 15:42